How do I determine this function??

he volume of a cone of radius r and height h is one-third the volume of a cylinder with the same radius and height. Does the su

antoniya [11.8K]

Answer:

The surface area of a cone of radius r and height h not equal to one-third the surface area of a cylinder with the same radius and height.

Relationship is $S_c=(\frac{\sqrt{(r+h)}}{2h})S_C$

Step-by-step explanation:

Given : The volume of a cone of radius r and height h is one-third the volume of a cylinder with the same radius and height.

To find : Does the surface area of a cone of radius r and height h equal one-third the surface area of a cylinder with the same radius and height?

If not, find the correct relationship. Exclude the bases of the cone and cylinder.

Solution :

Radius of cone and cylinder is 'r'.

Height of cone and cylinder is 'h'.

The volume of cone is $V_c=\frac{1}{3}\pi r^2 h$

The volume of cylinder is $V_C=\pi r^2 h$

$\frac{V_c}{V_C}=\frac{\frac{1}{3}\pi r^2 h}{\pi r^2 h}$

$V_c=\frac{1}{3}V_C$

i.e. volume of cone is one-third of the volume of cylinder.

Now,

Surface area of the cone is $S_c=\pi r\sqrt{(r+h)}$

Surface area of the cylinder is $S_C=2\pi rh$

Dividing both the equations,

$\frac{S_c}{S_C}=\frac{\pi r\sqrt{(r+h)}}{2\pi rh}$

$\frac{S_c}{S_C}=\frac{\sqrt{(r+h)}}{2h}$

$S_c=(\frac{\sqrt{(r+h)}}{2h})S_C$

Which clearly means $S_c\neq \frac{1}{3}S_C$

i.e. The surface area of a cone of radius r and height h not equal to one-third the surface area of a cylinder with the same radius and height.

The relationship between them is

$S_c=(\frac{\sqrt{(r+h)}}{2h})S_C$

4 0

3 years ago

Do przygotowania ćwierć litra soku potrzebne są 4 marchewki. Ile marchewek potrzeba żeby otrzymać pół litra soku, litr soku, 2li

Alina [70]

Answer:

Part 1) 8 carrots

Part 2) 16 carrots

Part 3) 32 carrots

Part 4) 48 carrots

Step-by-step explanation:

The question in English is

4 carrots are needed to prepare a quarter liter of juice. How many carrots do you need to get half a liter of juice, a liter of juice, 2 liters of juice, 3 liters of juice

Part 1) How many carrots do you need to get half a liter of juice?

we know that

4 carrots are needed to prepare 1/4 liter of juice

so

using proportion

Find out how many carrots do you need to get 1/2 liter of juice

$\frac{4}{(1/4)}=\frac{x}{(1/2)}\\\\x=4(1/2)/(1/4)\\\\x=8\ carrots$